With no political solution in sight, Congress faces another deadline to fund the Homeland Security Department by midnight Friday – a do-over of last week's bitter battle as Republicans try to stop President Obama's immigration plans.

The Republican-led House and Senate narrowly avoided a crisis late last week by compromising with Democrats to temporarily fund the department, which oversees the nation's vast domestic security and anti-terrorism apparatus, for seven more days.

Republican leaders vowed to continue pursuing their strategy because they view Obama's attempt to defer deportations for up to 5 million immigrants who are in the U.S. illegally as an abuse of executive power.

So far, the Republican strategy has failed in the face of Democratic opposition, as most members of the president's party agree with Obama's action.

Moreover, Republican leaders have struggled to form a coherent way out of the impasse.

Senate Republicans last week joined Majority Leader Mitch McConnell (R-Ky.) and agreed to a bipartisan bill with Democrats to fund the department until September, and put the immigration fight on a separate track. But Republicans in the House under Speaker John A. Boehner (R-Ohio) balked.

Republican leaders now want the House and Senate to go to a conference committee to resolve their differences, but that effort failed Monday.

McConnell opened the Senate on Monday as Republicans sought support from the handful of Democratic senators who have publicly disagreed with the president over his immigration action.

"This week promises to be a busy one," McConnell said. "I'd invite our Democratic friends to drop all the negativity and drop all the gridlock – join Republicans in advancing a positive agenda for the American people."

Most Democrats filibustered Monday evening's vote, however, preferring to fund the Homeland Security Department now and hold a separate immigration debate.

Senate Minority Leader Harry Reid (D-Nev.) explained that Democrats were blocking the conference committee move because "it will be counterproductive" and fail to produce a compromise, so long as Republicans insist on adding the restrictions on immigration.

"Senate Democrats will not be a party to yet another Republican charade that will inevitably shut down the Department of Homeland Security and put our nation at risk," Reid said.

The measure failed to advance, 47 to 43, a party-line vote that was short of the 60 needed. A separate vote to table the bill – in essence punting the issue back to the House – passed with a simple majority, 58 to 31– as McConnell and Republican leaders joined Democrats.

The outcome left Congress at a stalemate, with funding now set to expire again Friday.

Homeland Security Secretary Jeh Johnson has pleaded with Congress to provide stable funding for his department, which oversees the border, airport screenings, the Coast Guard, the Secret Service and other crucial security operations.

Officials said more than 200,000 employees of front-line agencies would be required to show up for work without pay if Congress fails to act.

But thousands of others would be furloughed, and numerous services and offices would be shut down across the country until the budget is restored. Though back pay is often provided after shutdowns, it is not guaranteed.

Boehner and his leadership were set to assemble their majority early Tuesday for a meeting. And late Monday, former Vice President Dick Cheney met at the Capitol with a group of key GOP lawmakers headed by Majority Whip Steve Scalise (R-La.), who is responsible for rounding up votes on bills.

Cheney, who had been invited almost a month ago to talk about foreign policy, was himself a whip when he served in the House.

As the week headed toward a repeat of last week's showdown, which wasn't resolved until just hours before the midnight funding deadline, some lawmakers held out hopes that cooler heads would prevail. The House is set to recess by Thursday afternoon so lawmakers can spend the following week away from Washington, and many lawmakers already have fundraisers and events planned in their home districts.

But with a new deadline ahead, Congress may be more likely to push the issue to the brink.

Staff writer Michael A. Memoli in Washington contributed to this story. For the latest from Congress follow @LisaMascaro